Need help with taking derivative + simplying a function

y = (2x-3)^2 / (x^3 - 7)^3

I used the quotient + chain rule to expand it out and got:

[(4(x^3)^3 (2x-3)) - ((9x^2)(2x-3)^2 (x^3 -7)^2)] / (x^3 - 7)^6

I *think* thats right, but if anyone wants to check it, I'd appreciate it. However, I'm having trouble simplifying from there. I think I can take out a common factor of (2x-3)(x^3 -7)^2 ? If so, what can I do from there? If not, what do I do?

Sorry if the equations looks messy I haven't learned how to use that code to make it look good yet.

I *think* thats right (unfortunately no. See correction in red), but if anyone wants to check it, I'd appreciate it. However, I'm having trouble simplifying from there. I think I can take out a common factor of (2x-3)(x^3 -7)^2 ? If so, what can I do from there? If not, what do I do?

Sorry if the equations looks messy I haven't learned how to use that code to make it look good yet.

Thanks in advance for any help.
-Jackson

Factor out (x^3-7)^2 in the numerator and split the denominator into (x^3-7)^2 * (x^3-7)^4 and then cancel the common factor.